it is possible .....
"Depending on the depth of the scratch start with 1200 wet and dry carborundum paper and rub with a little water until scratches are removed. Then use finer paper, e.g. 4000 followed by 3µm diamond paste or powder. Put the paste/ powder on fine, tightly woven cloth and rub until the glass/ metal becomes clear. If using powder moisten the cloth with water. Finish off with 1µm diamond paste/ powder. Always rinse when changing the medium. Smaller scratches can be polished with 6, 3, and 1µm diamond paste/ powder."
but it takes forever ..... buy a new mirror or don't worry about it
rossv